At the instant of midnight of New Year’s Eve on the Greenwich meridian, or when the mean sun is at the 180th meridian, American navigators on the seven seas will commence using a new type Nautical Almanac. It is well for those concerned not to neglect gaining some acquaintance with the new almanac before it becomes necessary to use it. Navigators aboard ships along the western coast of South America and in the Indian Ocean will be among the first to use the new type almanac. Those on the west coast of South America will need it for evening sights December 31, 1949, and those in the Indian Ocean will use it for morning sights January 1, 1950. It is easily possible that both the present and the new type almanacs will have to be used for calculating a round of sights, some observations being made a short time before and some shortly after the instant of Greenwich midnight.
It is predicted that the new type almanac will be enthusiastically received by those who have found it necessary to thumb through numberless pages and make many mental and arithmetical interpolations to solve a round of sights with the present almanac. Under the arrangement in the new almanac the Greenwich hour angle and declination .can always be found with two openings of the book. The altitude corrections have also been simplified. Interpolation is not required and parallax and semidiameter of the moon need not be found! The time necessary for working out sights will probably be cut in half. It may have some deflationary effect upon the ego of the navigator, who has always been regarded as somewhat of a savant aboard ship. With the advent of the new type almanac and the use of H.O. 211, H.O. 214, etc., for the solution of the astronomical triangle, the work of the navigator is simplified to such an extent that it can more easily be mastered.
The 1950 almanac represents a development of 100 years in almanac making. The authority for the preparation and publication of the American Ephemeris and Nautical Almanac was granted by Congress in 1849, and first publication was for the year 1855. In 1858, when the need was seen for a more concise book for navigators, the parts of the American Ephemeris and Nautical Almanac which are required for navigation were reprinted in a separate volume as the American Nautical Almanac. In 1916 the almanac was completely revised and especially designed for the convenience of navigators. None of it was reprinted from the American Ephemeris. Supplements to the Nautical Almanac were issued in 1930 and 1931 giving the Greenwich hour angle of the moon, the first time this appeared in any almanac. In 1932 the Greenwich hour angle of the moon was incorporated in the regular almanac, and in 1934 the Greenwich hour angles of the sun, Venus, Mars, Jupiter, Saturn, and 55 stars were included. Since 1934 up to the present there has been no material change. The 1950 almanac is a complete revision prepared under the supervision of G. M. Clemence, Director of the Nautical Almanac Office of the United States Naval Observatory. The accuracy of the new almanac is at least equal to the present Nautical Almanac, and in some cases greater.
A sample of all types of tables found in the 1950 almanac is shown herewith, except the Sun's Upper Limb Correction table, Polaris tables, and Conversion of Arc to Time table. The almanac contains 288 pages. In the front section of the book two facing pages, referred to as left-hand and right-hand pages, give complete data for three days. Table (1) is found on the left-hand pages and tables (2), (3), (4), (7), (8), (9), and (10) are printed on the right-hand pages. In the second section, the yellow tables (12), so named because they are printed on yellow paper, contain 60 tables, one for each minute of the hour. One part (consisting of the first four columns) has 60 lines, one for every second of the minute, and is used to bring the hourly value of the Greenwich hour angle (GHA) up to the minute and second of observation. The other part (making up the last three columns), with 180 values, is for use in bringing the hourly value of the declination up to the minute of observation, and also for obtaining small corrections to the GHA of the planets and the moon. Altitude Correction table for the moon (6) is found on the back cover and other altitude correction tables (5) are printed on the front cover. Additional Altitude corrections table (4) for the sun, moon, Venus and Mars are found on the right-hand daily pages. A list of 57 stars (11) numbered in order of their right ascensions is printed on the front cover.
Correcting Sextant Altitudes (hs) to Obtain Corrected Altitudes (Ho). (Marine Sextant).
The Nautical Almanac tables for correcting sextant altitudes (hs) are critical-type tables, the limiting entering arguments for each correction being given, and no interpolation is necessary.
Stars and Planets (5). This table corrects for refraction (R) only. It does not exactly agree with Table A of the present almanac because calculations are more exact.
Sun’s Lower Limb. (5). This table corrects for refraction (R), parallax (P) and the smallest annual semidiameter (SD), 15.7'. Additional Corrections table (4) corrects for increased SD for date. Combined, these tables give the same corrections as Table A and B in the present Almanac.
Height of Eye (5). This table corrects for dip (D) only and takes the place of Table C in the present almanac.
Corrections for Observed Altitude of the Moon (6). This table corrects for refraction (R) and parallax (P) for the center of the moon using the horizontal parallax (HP), 57.0', about average for the year. This table together with the Additional Corrections table (4) take the place of Table D in the present almanac. The Additional Altitude Corrections table for the moon corrects for SD, and P based on a HP differing from 57.0'.
Additional Altitude Corrections table (4) for Venus and Mars correct for parallax. These corrections are usually disregarded in the present almanac.
If the upper limb of the sun has been observed, correct the hs as if the lower limb had been observed and apply corrections given in the table page 250 (not shown here) in the Nautical Almanac. The table, as such, is not used in the present almanac, because in it the SD for date is given.
Corrections to hs to Obtain Ho. (Bubble Sextant). If the center of the sun or moon has been obtained (as with the bubble sextant), calculate the corrections for the two limbs separately and take the average of the two results, omitting dip corrections.
For stars and planets calculate Ho as for a marine sextant, omitting dip corrections.
The methods given above take the place of Tables E and F in the present almanac.
Corrections for hs to obtain Ho using a marine sextant are summarized below:
|
Body |
Daily pages |
Front Cover |
Back Cover |
|
Sun |
Add’l |
Sun’s Lower Limb, Ht. of eye |
Alt. Corr. |
|
Moon |
Add’l |
Ht. of eye |
|
|
Venus, Mars |
Add’l |
Stars & Planets, Ht. of eye |
|
|
Stars, Jupiter, Staturn |
|
Stars & Planets, Ht of eye |
In addition, index correction (IC) must be known and applied to all sights.
Example.—On January 1, 1950 the following observations are made from a height of eye of 50 feet with a marine sextant having an IC of (+) 1.5'; Sun, hs 10°15.2'; lower limb of moon, hs 47°23.0'; Venus, hs 10°33.4'; Jupiter, hs 9°56.0'; Rigel, hs 10°30.2\
Required: Ho for each body using the Nautical Almanac.
(Note: The examples given in this article may not be realistic due to the shortness of the sample tables, but they will serve well as “armchair” problems.)
Notes on solution:
In the Additional Altitude Corrections table on the right-hand daily pages, note that the data given for the sun, Venus, and Mars are considered sufficiently accurate for the three days on the page, and that corrections for Venus and Mars change with altitude. Also note that the moon corrections change with date.
When the altitude or height of eye corresponds exactly to the printed value in the critical tables found on the front cover and the right-hand daily pages under Additional Altitude Corrections, use the upper of the two possible corrections.
On the back cover page, if the minutes of altitude fall between 0.0' and 8.0', use the first column of corrections; if between 8.0' and 15.0' use the second column; etc. If the minutes are exactly 0.0', 8.0', 15.0', etc., use the right-hand column of the two possible corrections.
Finding the Greenwich Hour Angle
The Greenwich hour angle (GHA) of the vernal equinox (T) and the GHA of the sun, moon, and planets are tabulated at one hour intervals of GCT on the daily pages (1), (2). The increase in GHA for additional minutes and seconds is obtained from the yellow tables (12).
Example.—Find the GHA of the sun at GCT 10h44m03s on January 1, 1950.
Solution:
|
GCT |
10-44-03 |
Jan. 1 |
|
10h 44m C3s |
329-08.3 11-00.8 |
(2) (12) |
|
GHA |
340-09.1 |
|
In order to avoid code corrections (explained later) for the GHA of the sun, the tabulated hourly values are not entirely correct but become exactly correct when interpolated in the yellow tables at the half hour. The maximum tabular error for the sun’s GHA is 0.15'.
Example.—Find the GHA of the moon at GCT 3h45m16s on January 1, 1950.
Solution:
|
GCT |
3-45-16 |
Jan. 1 |
|
3h 45m 16s Corr |
85-07.7 10-48.1 |
Code (+) 109 (12) |
|
GHA |
96-04.1 |
|
The minimum hourly increase in GHA for the moon is 14°19.0' and this value is used for calculating the moon column in the yellow tables. The code number is the hourly variation in GHA minus 14°19.0' times 10. This code number is used as the entering argument in the yellow code corr’n columns to obtain the code correction. The code numbers for the moon are always plus (+) and never greater than 180, the highest entering argument in the code correction tables.
Example.—Find the GHA of Jupiter at GCT 8h45ml 7s on January 1, 1950.
Solution:
|
GCT |
8-45-17 |
Jan. 1 |
|
8h 44m 17s Corr |
271-16.7 11-19.3 1.4 |
Code (+) 19 |
|
GHA |
340-09.1 |
|
The GHA code number for a planet is similar in principle to that of the moon. It is 10 times the amount by which the increase in GHA between 1200 and 1300 of the middle day on the page exceeds 15°00.0'. The code number thus obtained is sufficiently accurate for all hours of the three days on the page. Occasionally, the hourly motion of Venus is less than 15°00.0', and in that case the code number is minus ( —), and the correction will have to be subtracted. The code numbers for planets are given at the bottom of the page.
Example.—Find the GHA of Caph (Star No. 2) at GCT 11h44m18s on January 1,1950.
Solution:
|
GCT |
11-44-18 |
Jan. 1 |
|
11h 44-18 SHA |
365-31.6 11-06.3 358-22.9 |
(1) †
(3) |
|
Sum GHA |
635-00.8 275-00.8 |
|
To obtain the GHA of a star the formula GHA-& = GHAT + SHA^ is used. The GHAT here is the sum of 265°31:6 and 11°06:3. The SHA^ is added to these values, subtracting 360° to obtain the GHA. There is no code correction since the hourly increase in GHA for the T is constant.
Declination of Navigational Bodies
The declinations of navigational bodies, except stars, are tabulated at one hour intervals of GCT on the daily pages (1), (2). Code numbers with algebraic signs are found at the bottom of the columns. The declination of stars is given for each 3-day period (3).
Example.—Find the declination of the sun, moon, Mars, and Ruchbah (star No. 4) at GCT 4h45m18* on January 1, 1950.
Solution:
|
Sun |
||
|
GCT |
4-45-18 |
Jan. 1 |
|
4h Corr |
(-)23-03.5 (+) 0.2 |
Code (+)2 |
|
d |
23-03.3 |
S |
|
Moon |
||
|
GCT |
4-45-18 |
Jan. 1 |
|
4h Corr |
(+)24-40.6 (+) 5.7 |
Code (+)75 |
|
d |
24-46.3 |
N |
|
Mars |
||
|
GCT |
4-45-18 |
Jan. 1 |
|
4h Corr |
(+) 1-24.2 (-) 0.2 |
Code (-)3 |
|
d |
1-24.0 |
N |
|
|
Ruchbah |
Star No. 4 |
|
GCT |
4-45-18 |
Jan. 1 |
|
d |
59.58.0 |
N |
The code numbers with algebraic signs for the sun and planets are obtained by subtracting the 1200 tabulated declination from the 1300 tabulated declination for the middle day and multiplying the result by 10. Since the hourly variation in the declination of the moon changes considerably for the three days, the code number (the hourly variation times 10) with algebraic sign, is given for every hour at the right of the table (1). The declinations of stars change very slowly and the change for a 3-day period is negligible.
Note that the tabulated hourly declination and the code correction are combined algebraically in the above solutions. A plus (+) correction means that the body is farther north than the tabulated declination and a minus (-) correction means that the body is farther south than the tabulated declination.
Example.—On January 1, 1950, the 0445 DR position of a ship is L 30°56.1' S, 65035.1' E. About this time the navigator observes Mars with a marine sextant, as follows: W 4h 45m 06s, WE on ZT 129 slow, height of eye 52 feet, IC ( -) 1.0', hs 57°11.7'.
Required: Solve the observation for a, Zn, and AP.
A complete solution with the Nautical Almanac and H.O. 214, Ad only, using a suggested form is given on the adjacent page.
Tables for Sunrise, Sunset and Twilight (7), Moonrise and Moonset (8), Equation of Time (9), and GCT of Transit (10) are given on the right-hand daily pages. These tables are self-explanatory. Sunrise, etc., are given for the middle day and considered sufficiently accurate for the three days on the page.
“Explanations and Examples” and tables for Sun’s Upper Limb, Conversion of Arc to Time, Latitude by Polaris and Azimuth of Polaris are given on pages prior to the yellow pages.
Additional notes on the Nautical Almanac
1. Yellow Tables are used only to facilitate arithmetical interpolations.
2. The Second and Third Correction tables for Polaris have no counterpart in the present almanac.
3. The last digit of a code is in tenths, (code 123 = 12.3').
4. To find the HP for date, add to 57.0' the value obtained from the daily pages, moon’s lower limb, the value for 0° minus the value for 90°.
Example: On January 1, HP = 57.0' + (13.1—15.0) = 57.0' —1.9'= 55.1'.
5. To find the SD of the moon for date, read the value on the daily pages for altitude 90°.
6. To find SD of the sun for date, add daily correction for the sun in Additional Altitude Correction tables to 15.7', the SD used for sun on the Front Cover page.
7. To find RA for bodies except stars at any hour, use the formula RA=GHAT – GHA.
8. To find RA of a star subtract SHA from 360°.
9. Note that SHA and Dec. recorded on the inserted sheet are only approximate— Use daily pages for exact values.
10. The dots placed at 3h, 9h, 15h, and 21h, facilitate the reading of the tables. Note that there are numbers, dots or algebraic signs at each 3-hour interval for declinations of bodies.
11. Phenomena. The Nautical Almanac (1950) gives the dates for the phases of the moon, and certain ecclesiastical and secular holidays. This information is found on the lower right-hand corner of the right-hand daily pages. Time and dates for solar eclipses are also found in the moon column of the left-hand daily pages. A star chart based on the sidereal hour angle is given on the last page of the almanac, where it will be most convenient for reference.